Hi, Theoretically ..... possible. But I kind of feel uncomfortable using 'with' as subjunctive.
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[3] (?) With X, he can solve the toughest puzzle.That's an interesting point. But couldn't we say that "the toughest puzzle" implies "any puzzle in #3"?
[4] (?) With X, he cannot solve the easiest puzzle.
A quantificational reading (such as 'ANY puzzle') is not available in [3] and [4].